7 files changed, 15 insertions, 8 deletions
diff --git a/core/math/face3.cpp b/core/math/face3.cpp
index d9d99b0384..6a15feefe1 100644
--- a/core/math/face3.cpp
+++ b/core/math/face3.cpp
@@ -136,7 +136,7 @@ Face3::Side Face3::get_side_of(const Face3 &p_face, ClockDirection p_clock_dir)
 
 		const Vector3 &v = p_face.vertex[i];
 
-		if (plane.has_point(v)) //coplanar, dont bother
+		if (plane.has_point(v)) //coplanar, don't bother
 			continue;
 
 		if (plane.is_point_over(v))
diff --git a/core/math/geometry.cpp b/core/math/geometry.cpp
index ec4d352a8f..97579e41ef 100644
--- a/core/math/geometry.cpp
+++ b/core/math/geometry.cpp
@@ -990,7 +990,7 @@ void Geometry::make_atlas(const Vector<Size2i> &p_rects, Vector<Point2i> &r_resu
 
 	//super simple, almost brute force scanline stacking fitter
 	//it's pretty basic for now, but it tries to make sure that the aspect ratio of the
-	//resulting atlas is somehow square. This is necesary because video cards have limits
+	//resulting atlas is somehow square. This is necessary because video cards have limits
 	//on texture size (usually 2048 or 4096), so the more square a texture, the more chances
 	//it will work in every hardware.
 	// for example, it will prioritize a 1024x1024 atlas (works everywhere) instead of a
@@ -1057,7 +1057,7 @@ void Geometry::make_atlas(const Vector<Size2i> &p_rects, Vector<Point2i> &r_resu
 			if (end_w > max_w)
 				max_w = end_w;
 
-			if (ofs == 0 || end_h > limit_h) //while h limit not reched, keep stacking
+			if (ofs == 0 || end_h > limit_h) //while h limit not reached, keep stacking
 				ofs += wrects[j].s.width;
 		}
 
diff --git a/core/math/geometry.h b/core/math/geometry.h
index 93ab0be2e0..26f977e6eb 100644
--- a/core/math/geometry.h
+++ b/core/math/geometry.h
@@ -108,7 +108,7 @@ public:
 		//do the function 'd' as defined by pb. I think is is dot product of some sort
 #define d_of(m, n, o, p) ((m.x - n.x) * (o.x - p.x) + (m.y - n.y) * (o.y - p.y) + (m.z - n.z) * (o.z - p.z))
 
-		//caluclate the parpametric position on the 2 curves, mua and mub
+		//calculate the parametric position on the 2 curves, mua and mub
 		real_t mua = ( d_of(p1,q1,q2,q1) * d_of(q2,q1,p2,p1)  - d_of(p1,q1,p2,p1) * d_of(q2,q1,q2,q1) ) / ( d_of(p2,p1,p2,p1) * d_of(q2,q1,q2,q1)  - d_of(q2,q1,p2,p1) * d_of(q2,q1,p2,p1) );
 		real_t mub = ( d_of(p1,q1,q2,q1) + mua * d_of(q2,q1,p2,p1)  ) / d_of(q2,q1,q2,q1);
 
diff --git a/core/math/matrix3.cpp b/core/math/matrix3.cpp
index 5f73d91ef3..b31df2fadb 100644
--- a/core/math/matrix3.cpp
+++ b/core/math/matrix3.cpp
@@ -229,7 +229,7 @@ Vector3 Basis::get_scale() const {
 	// FIXME: We eventually need a proper polar decomposition.
 	// As a cheap workaround until then, to ensure that R is a proper rotation matrix with determinant +1
 	// (such that it can be represented by a Quat or Euler angles), we absorb the sign flip into the scaling matrix.
-	// As such, it works in conjuction with get_rotation().
+	// As such, it works in conjunction with get_rotation().
 	real_t det_sign = determinant() > 0 ? 1 : -1;
 	return det_sign * Vector3(
 							  Vector3(elements[0][0], elements[1][0], elements[2][0]).length(),
@@ -575,6 +575,8 @@ Basis::Basis(const Quat &p_quat) {
 Basis::Basis(const Vector3 &p_axis, real_t p_phi) {
 	// Rotation matrix from axis and angle, see https://en.wikipedia.org/wiki/Rotation_matrix#Rotation_matrix_from_axis_and_angle
 
+	ERR_FAIL_COND(p_axis.is_normalized() == false);
+
 	Vector3 axis_sq(p_axis.x * p_axis.x, p_axis.y * p_axis.y, p_axis.z * p_axis.z);
 
 	real_t cosine = Math::cos(p_phi);
diff --git a/core/math/plane.cpp b/core/math/plane.cpp
index 29e7f2e75c..bef5c3ab06 100644
--- a/core/math/plane.cpp
+++ b/core/math/plane.cpp
@@ -116,7 +116,7 @@ bool Plane::intersects_ray(Vector3 p_from, Vector3 p_dir, Vector3 *p_intersectio
 	real_t dist = (normal.dot(p_from) - d) / den;
 	//printf("dist is %i\n",dist);
 
-	if (dist > CMP_EPSILON) { //this is a ray, before the emiting pos (p_from) doesnt exist
+	if (dist > CMP_EPSILON) { //this is a ray, before the emitting pos (p_from) doesn't exist
 
 		return false;
 	}
diff --git a/core/math/rect3.h b/core/math/rect3.h
index 26198537c2..0b11cd7b52 100644
--- a/core/math/rect3.h
+++ b/core/math/rect3.h
@@ -95,7 +95,7 @@ public:
 
 	Rect3 expand(const Vector3 &p_vector) const;
 	_FORCE_INLINE_ void project_range_in_plane(const Plane &p_plane, real_t &r_min, real_t &r_max) const;
-	_FORCE_INLINE_ void expand_to(const Vector3 &p_vector); /** expand to contain a point if necesary */
+	_FORCE_INLINE_ void expand_to(const Vector3 &p_vector); /** expand to contain a point if necessary */
 
 	operator String() const;
 
diff --git a/core/math/vector3.h b/core/math/vector3.h
index fc02e66c33..951380e898 100644
--- a/core/math/vector3.h
+++ b/core/math/vector3.h
@@ -75,6 +75,7 @@ struct Vector3 {
 
 	_FORCE_INLINE_ void normalize();
 	_FORCE_INLINE_ Vector3 normalized() const;
+	_FORCE_INLINE_ bool is_normalized() const;
 	_FORCE_INLINE_ Vector3 inverse() const;
 
 	_FORCE_INLINE_ void zero();
@@ -214,7 +215,7 @@ real_t Vector3::distance_squared_to(const Vector3 &p_b) const {
 
 real_t Vector3::angle_to(const Vector3 &p_b) const {
 
-	return Math::acos(this->dot(p_b) / Math::sqrt(this->length_squared() * p_b.length_squared()));
+	return Math::atan2(cross(p_b).length(), dot(p_b));
 }
 
 /* Operators */
@@ -385,6 +386,10 @@ Vector3 Vector3::normalized() const {
 	return v;
 }
 
+bool Vector3::is_normalized() const {
+	return Math::isequal_approx(length(), (real_t)1.0);
+}
+
 Vector3 Vector3::inverse() const {
 
 	return Vector3(1.0 / x, 1.0 / y, 1.0 / z);